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DOE OSTI2014

WE-A-BRF-01: Dual-Energy CT Imaging in Diagnostic Imaging and Radiation Therapy

The quantification accuracy of dual-energy imaging is influenced by the fundamentals of x-ray physics, system geometry, data acquisition hardware/protocol, system calibration, and image processing technique. This symposium will provide updates on the following advanced application areas: Mammography. Volumetric breast density techniques based on standard mammograms require estimation of breast thickness, which is difficult to accurately measure. By comparison, calculation of breast density using dual energy mammography does not require measurement of breast thickness. Dual energy mammography has been implemented using both energy integrating flat panel detectors in conjunction with beam energy switching and energy resolved photon counting detectors. These techniques have been optimized using simulation studies and validated using physical phantoms and postmortem breasts. Chemical decomposition was used as the gold standard for volumetric breast density measurement in postmortem breasts. Breast density measurements have also been compared with results from four-category BI-RADS density rankings, standard image thresholding and Fuzzy k-mean clustering techniques. These studies indicate that dual energy mammography can be used to accurately measure volumetric breast density. Cardiovascular CT. The predicative accuracy of risk models for recurrent stroke and cardiac arrest depends heavily on accurate differentiation of thrombus or calcium from iodine in left atrial appendage or coronary arteries. The amount of energy separation is constrained by image noise; therefore, optimal kVp, beam filtration, and balanced flux are essential for the quantification accuracy of iodine and calcium. The basis materials are combined linearly to generate monochromatic energy images, where CT# accuracy and CNR are energy dependent. With optimal monochromatic energy, the mean iodine concentration for the thrombus, circulatory stasis, and control groups are significantly different. Risk classification based on calcium scores shows excellent agreement with classification on the basis of conventional coronary artery calcium scoring. These studies demonstrate dual-energy cardiovascular CT can potentially be a noninvasive and sensitive modality in high risk patients. On-board KV/MV Imaging. To enhance soft tissue contrast and reduce metal artifacts, we have developed a dual-energy CBCT technique and a novel on-board kV/MV imaging technique based on hardware available on modern linear accelerators. We have also evaluated the feasibility of these two techniques in various phantom studies. Optimal techniques (energy, beam filtration, # of overlapping projections, etc) have been investigated with unique calibration procedures, which leads to successful decomposition of imaged material into acrylic-aluminum basis material pair. This enables the synthesis of virtual monochromatic (VM) CBCT images that demonstrate much less beam hardening, significantly reduced metal artifacts, and/or higher soft tissue CNR compared to single-energy CBCT. Adaptive Radiation Therapy. DECT could actually contribute to the area of Dose-Guided Radiation Therapy (or Adaptive Therapy). The application of DECT imaging using 80kV and 140 kV combinations could potentially increase the image quality by reducing the bone or high density material artifacts and also increase the soft tissue contrast by a light contrast agent. The result of this higher contrast / quality images is beneficial for deformable image registration / segmentation algorithm to improve its accuracy hence to make adaptive therapy less time consuming in its recontouring process. The real time re-planning prior to per treatment fraction could become more realistic with this improvement especially in hypofractional SBRT cases. Learning Objectives: Learn recent developments of dual-energy imaging in diagnosis and radiation therapy; Understand the unique clinical problem and required quantification accuracy in each application; Understand the different approaches to optimize dual-energy imaging techniques for different applications.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

CERN’s Linac4 H{sup −} sources: Status and operational results

Two volume sources equipped with DESY and CERN plasma generators and a low voltage electron dump were operated at 45 kV in the Linac4 tunnel and on a dedicated test stand. These volume sources delivered approximately 20 mA and ensured the commissioning of the Radio Frequency Quadrupole accelerator and of the first section of the Drift Tube Linac. CERN’s prototype of a cesiated surface source equipped with this electron dump was operated continuously from November 2013 to April 2014 on the ion source test stand and is being commissioned in the Linac4 tunnel. Before cesiation, the prototype conditioned in volume mode provided up to 30 mA H{sup −} beam. Short cesiations, of the order of 10 mg effectively reduced the intensity of co-extracted electrons down to 2 - 8 times the H{sup −} current; this cesiated surface operation mode delivered up to 60 mA H{sup −} beam. An H{sup −} beam of the order of 40 mA was sustained up to four weeks operation with 500 μs pulses at 1.2s spacing. A new extraction was designed to match these beam properties. A copy of BNL’s magnetron produced at CERN was tested at BNL and delivered at 40 kV H{sup −} beam exceeding Linac4’s nominal intensity of 80 mA. In this contribution, the performances, dynamic response to cesiation, stability and availability of these prototypes are described. The needed optimization of the emittance of H{sup −} beam above 40 mA is presented, which requires an evolution of the front end that encompasses implementation of a large ceramic insulator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

SU-F-T-591: SBRT Treatment of Multiple Extracranial Oligometastases Using a Single-Isocenter with Distinct Optimizations (SIDO)

Purpose: A new development in linac-based intracranial radiosurgery is treatment of multiple targets using single isocenter VMAT, which dramatically reduces treatment time while maintaining high conformality and dose gradient. Our purpose is to translate this technique to extracranial SBRT of oligometastases and address additional challenges such as interplay from motion and setup uncertainties. Methods: We propose SIDO (Single Isocenter with Distinct Optimizations) planning in which all VMAT arcs share an isocenter but each arc treats only one target. Setup uncertainties from rotations and deformations are mitigated by applying a couch translation between VMAT arcs, while interplay is minimized by using dynamic conformal arcs (DCAs) as the starting point for VMAT optimization. We compared SIDO to single (VMAT) and dual (VMAT & DCA) isocenter plans for phantom and patient (N=2) cases. Dose statistics included conformity index (CI), gradient index (GI), and modulation factor (MLC opening & total MU). Finally, we determined likelihood of needing a translational shift between SIDO arcs to correct rotational uncertainties using CBCTs from eleven previous SBRT cases. Results: For phantoms with target separations of 5–15cm, CI was 0.87±0.02, 0.89±0.05, and 0.91±0.02, for SIDO, single, and dual-isocenter VMAT respectively. GI was 6.83±1.0, 7.45±1.0 and 5.94±0.7 respectively. SIDO conformity did not trend with increasing distance between PTVs, while gradient decreased for all planning techniques. Using DCAs as the starting point of VMAT optimization decreased modulation, with a 39.4% reduction in monitor units. SIDO had 4.9% and 39% less MU than single and dual-isocenter VMAT respectively. A translational shift between SIDO arcs would be required in 10–28% of cases due to rotational uncertainties to stay within a 5mm margin, for targets separated by ≥10cm. Conclusion: SIDO for extracranial oligometastases has comparable dosimetry to traditional VMAT with low modulation similar to DCAs. Future work will quantify decrease in dosimetric interplay.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion

The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered often exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multi-physics systems: implicit time integration for efficient long term time integration of stiff multi-physics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton–Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A Solar-assisted Voltage Optimization Method for Transmission Solar Network Power System

This paper proposes a new formulation and solution algorithm that uses transmission level solar inverters to address the security-constrained optimal power flow (SCOPF) problem. The goal is to stabilize voltage fluctuations in transmission networks in base case and contingency scenarios, by using bulk solar power plant with a minimal number of post-contingency corrections. To achieve this goal, a two-stage volt/var optimization method is proposed to first correct all voltage violations with the volt-var alternating current optimal power flow (ACOPF) algorithm for a base case. Then a linearized SCOPF volt-var control algorithm is proposed to identify the corrective actions for all potential voltage violations in all contingency scenarios. The proposed method was tested and validated on a modified IEEE 118-bus system with solar photovoltaic (PV) data.

Photovoltaic, Volt/Var Control↗
DOE OSTI2020

Optimizing HVAC Operations in Multi-unit Buildings for Grid Demand Response

The thermal inertia of buildings, along with the flexibility associated with thermostatically controlled loads (TCL) allows heating ventilation and cooling (HVAC) systems to be used for grid demand response (DR). In this work, we consider an HVAC system that serves multiple units in a residential building to meet their space heating requirements. We aim to determine the optimal power flow to each unit that minimizes the power costs incurred by the building's occupants while keeping in consideration their thermal comfort. The DR program is assumed to allow the building temperatures to deviate from the set-points up to a maximum limit. Despite the complex, non-linear structure of the problem, we show how the optimal solutions can be obtained efficiently using quadratic programming. Since HVAC systems can run on either electricity or natural gas, we study the efficacy of the DR regime for both hourly electricity prices and flat gas prices over the course of 24 hours. Finally, we run simulations to determine the optimal thermal power and the evolution of unit temperatures for various energy pricing schemes.

Naqvi, Syed A.↗
DOE OSTI2026

Extremized nonlinear and linearized responses in soft metamaterials enabled by gradient-based design and grayscale digital light processing

In this study, we develop a gradient-based design approach that exploits grayscale digital light processing (DLP) 3D printing for extremizing the nonlinear and linearized response of soft metamaterials — materials that harness engineered geometric instabilities to undergo large and programmable changes in configuration. Grayscale DLP approaches modulate local mechanical properties at the pixel scale by tuning the light intensity within a single grayscale image, unlocking an exceptionally large design space. To effectively navigate this space, we develop smooth mappings between local light intensity values and global quantities of interest that characterize the behavior of soft metamaterials. Enabling these smooth mappings are robust and differentiable nonlinear finite element simulations powered by a trust region solver. A PDE-constrained optimization problem is then solved to invert these mappings and produce light intensity distributions that endow the printed part with varying stiffness and flexibility in distinctive regions. It is shown that optimizing the distribution of soft and stiff phases throughout a metamaterial structure results in markedly different buckling and self-contact configurations to drive extremized nonlinear compression and linearized vibration responses. Optimized light intensity distributions are translated to grayscale images and directly used to print soft metamaterial samples, showing remarkable agreement between the buckling and self-contact response in simulated and measured deformed configurations.

Additive manufacturing↗
DOE OSTI2016

Stochastic Predictions of Cell Kill During Stereotactic Ablative Radiation Therapy: Do Hypoxia and Reoxygenation Really Matter?

Purpose: To simulate stereotactic ablative radiation therapy on hypoxic and well-oxygenated in silico tumors, incorporating probabilistic parameter distributions and linear-quadratic versus linear-quadratic-cubic methodology and the evaluation of optimal fractionation schemes using biological effective dose (BED{sub α/β=10} {sub or} {sub 3}) comparisons. Methods and Materials: A temporal tumor growth and radiation therapy algorithm simulated high-dose external beam radiation therapy using stochastic methods. Realistic biological proliferative cellular hierarchy and pO{sub 2} histograms were incorporated into the 10{sup 8}-cell tumor model, with randomized radiation therapy applied during continual cell proliferation and volume-based gradual tumor reoxygenation. Dose fractions ranged from 6-35 Gy, with predictive outcomes presented in terms of the total doses (converted to BED) required to eliminate all cells that could potentially regenerate the tumor. Results: Well-oxygenated tumor control BED{sub 10} outcomes were not significantly different for high-dose versus conventional radiation therapy (BED{sub 10}: 79-84 Gy; Equivalent Dose in 2 Gy fractions with α/β of 10: 66-70 Gy); however, total treatment times decreased from 7 down to 1-3 weeks. For hypoxic tumors, an additional 28 Gy (51 Gy BED{sub 10}) was required, with BED{sub 10} increasing with dose per fraction due to wasted dose in the final fraction. Fractions of 9 Gy compromised well for total treatment time and BED, with BED{sub 10}:BED{sub 3} of 84:176 Gy for oxic and 132:278 Gy for non-reoxygenating hypoxic tumors. Initial doses of 12 Gy followed by 6 Gy further increased the therapeutic ratio. When delivering ≥9 Gy per fraction, applying reoxygenation and/or linear-quadratic-cubic cell survival both affected tumor control doses by a significant 1-2 fractions. Conclusions: The complex temporal dynamics of tumor oxygenation combined with probabilistic cell kinetics in the modeling of radiation therapy requires sophisticated stochastic modeling to predict tumor cell kill. For stereotactic ablative radiation therapy, high doses in the first week followed by doses that are more moderate may be beneficial because a high percentage of hypoxic cells could be eradicated early while keeping the required BED{sub 10} relatively low and BED{sub 3} toxicity to tolerable levels.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2024

A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to solutions with voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4,518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.

approximation algorithms↗
DOE OSTI2018

Data-Enabled Building Energy Savings (D-E BES)

Building sector energy consumption represents a significant fraction of the overall energy consumption in urban communities. While there has been increasing focus on the development of smart environments to support energy savings in urban commercial buildings, the development of smart environments for the residential sector has been less common. Instead, urban residential energy-saving efforts have focused on improving a building's physical infrastructure, introducing energy-saving appliances, and motivating residents to adopt energy conservation practices. Herein this paper illustrates that creating an affinity between a building resident's thermal preferences and a building apartment's unregulated thermal environment represents an alternative means of generating an energy-efficient environment for multi-family, residential buildings. Two years of 15-min interval summer data, obtained from smart cyber-physical systems installed in 310 apartments across two New York City buildings, is used to develop data-enabled (D-E) models of resident thermal preference and unregulated apartment temperatures. Both of these models use a linear mixed-effects approach. The alignment of optimal resident-apartment pairs is then formulated as an integer-programming problem to explore the building energy saving (BES) potential associated with minimizing the difference between unregulated apartment temperature and the residents' thermal preference based on summer cooling loads. The work shows that the energy saving potential vary with a building's physical characteristics as well as the variation in residents' thermal preferences. The work further demonstrates that both the unregulated temperature and the resident's preferred temperature in a given apartment are not only affected by outside temperature and external relative humidity, but also strongly affected by the apartment's geographic orientation. For the specific buildings considered, up to 28% cooling energy saving is possible with full alignment. The paper provides all building monitoring data as an open source data set.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

A tri-level distribution locational marginal price-based demand response framework

Here, in this paper, we propose a tri-level, nested, two-stage price-based demand response (PBDR) framework that considers distribution locational marginal price (DLMP) as DR enabler between load-serving entities (LSE), demand response providers (DRPs), and customers in the day-ahead distribution market. It enables LSE and customer interactions by using multiple DRPs, positioned in-between, and independently optimizes their objectives. The problem is formulated using linear power flow with approximated power losses and its application in DLMP as DR pricing. The tri-level problem is solved using a nested reformulation & decomposition (R&D) method and tested on the real Indian-108 bus distribution system under various dynamic pricings. Further, the temporal–spatial variations in DLMPs are assessed using fairness criteria. Numerical analyses demonstrate that DLMP applications can effectively improve economic efficiency, and transparency in DR programs valuation with a favorable fairness margin. The results show that DLMP as DR pricing signal induces (0-2) % variation in DLMP for DR participation up to 10 %. Further, it gives over 90 % fairness over temporal–spatial variation for all the customers.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Enabling Grid-Aware Market Participation of Aggregate Flexible Resources

Increasing integration of distributed energy resources (DERs) within distribution feeders provides unprecedented flexibility at the distribution-transmission interconnection. With the new FERC 2222 order, DER aggregations are allowed to participate in energy market. To enable market participation, these virtual power plants need to provide their generation cost curves. This paper proposes efficient optimization formulations and solution approaches for the characterization of hourly as well as multi-time-step generation cost curves for a distribution system with high penetration of DERs. Network and DER constraints are taken into account when deriving these cost curves, and they enable active distribution systems to bid into the electricity market. The problems of deriving linear and quadratic cost curves are formulated as robust optimization problems and tractable reformulation/solution algorithm are developed to facilitate efficient calculations. The proposed formulations and solution algorithm are validated on a realistic test feeder with high penetration of flexible resources.

aggregated distributed energy resources↗
DOE OSTI2025

A matheuristic for design and dispatch of a utility-connected distributed energy system

Modeling distributed power generation systems often requires complicated mathematical expressions that present challenges for commercial optimization solvers. Here, this paper presents a matheuristic to solve a mixed-integer optimization model that informs decisions regarding the design and dispatch of a utility-connected microgrid. We deploy a genetic algorithm to search the system design space and a linear program to solve the economic dispatch problem. The model is a component of a web tool that requires solutions within a few minutes. Our method yields objective function values within 5% of an exogenously produced optimal in fewer than 30 seconds for 90% of our test cases compared to only 10% of our test cases by a traditional optimization solver in the same amount of time.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2013

A unified RANS–LES model: Computational development, accuracy and cost

Large eddy simulation (LES) is computationally extremely expensive for the investigation of wall-bounded turbulent flows at high Reynolds numbers. A way to reduce the computational cost of LES by orders of magnitude is to combine LES equations with Reynolds-averaged Navier–Stokes (RANS) equations used in the near-wall region. A large variety of such hybrid RANS–LES methods are currently in use such that there is the question of which hybrid RANS-LES method represents the optimal approach. The properties of an optimal hybrid RANS–LES model are formulated here by taking reference to fundamental properties of fluid flow equations. It is shown that unified RANS–LES models derived from an underlying stochastic turbulence model have the properties of optimal hybrid RANS–LES models. The rest of the paper is organized in two parts. First, a priori and a posteriori analyses of channel flow data are used to find the optimal computational formulation of the theoretically derived unified RANS–LES model and to show that this computational model, which is referred to as linear unified model (LUM), does also have all the properties of an optimal hybrid RANS–LES model. Second, a posteriori analyses of channel flow data are used to study the accuracy and cost features of the LUM. The following conclusions are obtained. (i) Compared to RANS, which require evidence for their predictions, the LUM has the significant advantage that the quality of predictions is relatively independent of the RANS model applied. (ii) Compared to LES, the significant advantage of the LUM is a cost reduction of high-Reynolds number simulations by a factor of 0.07Re{sup 0.46}. For coarse grids, the LUM has a significant accuracy advantage over corresponding LES. (iii) Compared to other usually applied hybrid RANS–LES models, it is shown that the LUM provides significantly improved predictions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Hydropower flexibility valuation tool for flow requirement evaluation

Timing of generation is becoming more and more valuable. This creates greater potential tension between environmental and power system objectives since both systems require their own flow patterns. Identifying win–win outcomes in this context requires being able to discuss the value of flexibility across stakeholder groups. This research proposes a two-stage optimization method to understand hydropower flexibility to meet both environmental and power system requirements. The tool simulates the two-settlement market process in the U.S. by maximizing revenues from both the day-ahead and real-time markets, subject to plant operational limits, regulatory flow and ramping requirements, and uncertainties associated with water availability and market prices. The model is formulated as linear programming problems and solved using IBM ILOG CPLEX optimizer. By examining a range of flow requirements, ramping constraints, and storage capacities, the proposed tool shows how to make more informed decisions to weigh the cost of specific flow requirements in the context of the overall license requirements. Results from the case study show that revenue is more sensitive to the ramping constraints than the minimum flow constraints. We also demonstrate that removing flow constraints in a dry month increases monthly revenue by up to 118%, as opposed to only 1% in a wet month. In addition, our results suggest that using a learning-based water flow forecast results in an increase of monthly revenue up to 6.4% compared with persistence forecast.

13 HYDRO ENERGY↗
DOE OSTI2020

Atacama Cosmology Telescope: Component-separated maps of CMB temperature and the thermal Sunyaev-Zel’dovich effect

Optimal analyses of many signals in the cosmic microwave background (CMB) require map-level extraction of individual components in the microwave sky, rather than measurements at the power spectrum level alone. To date, nearly all map-level component separation in CMB analyses has been performed exclusively using satellite data. In this paper, we implement a component separation method based on the internal linear combination (ILC) approach which we have designed to optimally account for the anisotropic noise (in the 2D Fourier domain) often found in ground-based CMB experiments. Using this method, we combine multi-frequency data from the Planck satellite and the Atacama Cosmology Telescope Polarimeter (ACTPol) to construct the first wide-area, arcminute-resolution component-separated maps (≈ 2100 sq. deg.) of the CMB temperature anisotropy and the thermal Sunyaev-Zel'dovich (tSZ) effect sourced by the inverse-Compton scattering of CMB photons off hot, ionized gas. Our ILC pipeline allows for explicit deprojection of various contaminating signals, including a modified blackbody approximation of the cosmic infrared background (CIB) spectral energy distribution. The cleaned CMB maps will be a useful resource for CMB lensing reconstruction, kinematic SZ cross-correlations, and primordial non-Gaussianity studies. Here, the tSZ maps will be used to study the pressure profiles of galaxies, groups, and clusters through cross-correlations with halo catalogs, with dust contamination controlled via CIB deprojection. The data products described in this paper are available on LAMBDA.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Non-linear Model Predictive Control of Wave Energy Converters with Realistic Power Take-off Configurations and Loss Model

Model Predictive Control (MPC) has been recognized as a well-developed control strategy for optimizing the performance of wave energy converters (WECs). The standard problem involves maximizing the absorbed power from oncoming waves while respecting motion constraints of the device and force constraints of the power take-off (PTO). The generated electrical power is then calculated by assuming an ideal PTO with no power conversion losses or limitations to power flow. In this article, we remove the assumption of an ideal PTO and present four different control options that reflect unique combinations of PTO control and power flow constraints. We also recast the MPC problem to maximize the generated power instead of the absorbed power by accounting for the losses in the power train. Using a WEC with a hydraulic PTO, we develop a loss model suitable for controls optimization. Lastly, we illustrate the process of setting up the non-linear MPC problem and compare the performance of competing control strategies using a common benchmark based on annual energy captured at a reference site.

16 TIDAL AND WAVE POWER↗
DOE OSTI2016

Nature of size effects in compact models of field effect transistors

Investigations have shown that in the local approximation (for sizes L < 100 μm), AlGaN/GaN high electron mobility transistor (HEMT) structures satisfy to all properties of chaotic systems and can be described in the language of fractal geometry of fractional dimensions. For such objects, values of their electrophysical characteristics depend on the linear sizes of the examined regions, which explain the presence of the so-called size effects—dependences of the electrophysical and instrumental characteristics on the linear sizes of the active elements of semiconductor devices. In the present work, a relationship has been established for the linear model parameters of the equivalent circuit elements of internal transistors with fractal geometry of the heteroepitaxial structure manifested through a dependence of its relative electrophysical characteristics on the linear sizes of the examined surface areas. For the HEMTs, this implies dependences of their relative static (A/mm, mA/V/mm, Ω/mm, etc.) and microwave characteristics (W/mm) on the width d of the sink-source channel and on the number of sections n that leads to a nonlinear dependence of the retrieved parameter values of equivalent circuit elements of linear internal transistor models on n and d. Thus, it has been demonstrated that the size effects in semiconductors determined by the fractal geometry must be taken into account when investigating the properties of semiconductor objects on the levels less than the local approximation limit and designing and manufacturing field effect transistors. In general, the suggested approach allows a complex of problems to be solved on designing, optimizing, and retrieving the parameters of equivalent circuits of linear and nonlinear models of not only field effect transistors but also any arbitrary semiconductor devices with nonlinear instrumental characteristics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗